1. Introduction

In recent years, lithium niobate on insulator (LNOI) [1–4] has emerged as one of the most promising material platforms for integrated optics. Owing to its strong second-order nonlinearity (d₃₃ = 27 pm/V), relatively large refractive index contrast, low optical absorption, ultra-wide transparency spanning the ultraviolet to far-infrared, and unique ferroelectric properties, LNOI has become the foremost choice for second-order nonlinear optics. Diverse nonlinear optical processes enabled by LNOI include second harmonic generation (SHG) [5–14], sum- and difference-frequency generation [15,16], and parametric down conversion (PDC) [17–20], which play critical roles in coherent light generation at arbitrary wavelengths and nonclassical quantum state preparation [18]. Among these, SHG, which doubles the frequency of an incident field by harnessing the tight modal confinement of micronano waveguides and resonance enhancement in high-quality microcavities, has constituted an area of particular research focus.

The SHG process necessitates fulfilling phase matching conditions to occur efficiently. Numerous phase matching approaches have been realized on lithium niobate on insulator (LNOI), including birefringent phase matching [21], modal phase matching [7,10], cyclic phase matching [22,23], periodic geometry engineering [6], quasi phasematching via periodic poling [24–26]. Periodically poled lithium niobate (PPLN) currently constitutes the most effective platform for nonlinear frequency conversion. Using this approach, Lu et al. achieved the highest second harmonic generation (SHG) efficiency to date of 5,000,000%/W in a microring [17]. Cyclic phase matching typically necessitates ultrahigh-Q microdisk resonators (Q∼10⁶) [23] fabricated by specialized chemical-mechanical polishing, which can only couple to tapered fibers without on-chip integration. Modal phase matching for SHG has witnessed remarkable advancements on the lithium niobate on insulator (LNOI) platform. However, there are no suitable microresonators to enhance the efficiency to the desired level. The isotropic in-plane optical properties of Z-cut LNOI facilitate designing phase-matched microring cavities. Luo et al. attained 1500%/W normalized SHG conversion efficiency via microcavity-enhanced modal phase matching on Z-cut LNOI [15]. Chen et al. realized 26%/W/cm² SHG efficiency in phase-matched waveguides, demonstrating a 10-fold enhancement with microring resonators [10]. However, a single waveguide coupling to the microring cannot concurrently fulfill the critical coupling conditions for both the pump and the second harmonic (SH), limiting the attainable efficiency. Furthermore, microresonator-enhanced modal phase matching for SHG remains unexplored on X-cut LNOI, impeding integration of high-performance electro-optic modulators [27] and other devices enabled by this platform.

Here, we propose and experimentally validate enhancing SHG efficiency using a modal phase matched racetrack microring resonator (RMR) on X-cut LNOI. Independent couplers for the pump and second-harmonic enable simultaneous critical coupling. The RMR radius is tailored to preclude quality factor degradation from mode hybridization. Experimentally, the extracted loaded quality factors are $Q_{T{E_0}}^{1560nm} = 1 \times {10^5}$ and $Q_{T{E_2}}^{780nm} = 2.8 \times {10^4}$ for the interacting pump and SH modes. Precisely controlling the RMR temperature allows concurrent pump and SH resonance, further boosting conversion efficiency. At low pump power, a normalized efficiency of 9972%/W is attained. In our experiment, the microring resonator demonstrated a 25.73 dB enhancement in SHG efficiency compared to a 4 mm straight waveguide with the same mode phase matching design.

2. Design and simulation of double resonance RMR

As illustrated in Fig. 1(a), the schematic diagram depicts a double-resonance RMR on an X-cut LNOI wafer. The illustration in Fig. 1(a) shows the cross section of the waveguide, where the sidewall inclination of the lithium niobate waveguide is theta = 66°. This angle was precisely measured by scanning electron microscopy in our previous experiments, and is incorporated in subsequent simulations. The 1560 nm pump is coupled from the top waveguide into the RMR, where it experiences power enhancement and nonlinear frequency conversion facilitated by the ring resonator. The resulting 780 nm SH is out-coupled from the RMR through the bottom waveguide. The straight section of the RMR has a length of 600 µm, chosen to achieve phase matching between the TE₀ mode of the pump and the TE₂ mode of the SH light, which is $nef{f_{{\omega _1},TE0}} = nef{f_{{\omega _2},TE2}}$. This configuration allows efficient utilization of the maximum nonlinear coefficient d₃₃ and provides a relatively large mode overlap factor compared to the asymmetric TE₁ mode of the second harmonic light.

 

Fig. 1. (a) Schematic of double resonance RMR and the illustration shows the cross section of the LN waveguide. (b) Simulation of effective refractive index of pump and second harmonic light in straight waveguide. (c,d) Simulation of effective refractive index versus rotation angle in 180° curved waveguide. (e) FDTD simulation of TE₂ and TM₂ mode crosstalk for different bending radii. Insets show field distribution for radii of 26 µm and 30 µm.

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As shown in Fig. 1(b), by numerically solving the effective refractive index of intrinsic mode of the optical waveguide, it can be seen that when the waveguide width is 0.733 µm, the geometric dispersion of the waveguide can compensate the material dispersion to achieve phase matching between the two modes. The upper left illustration shows the mode field distribution of the two interacting modes. The X-cut LNOI has an anisotropic refractive index in the chip plane, with ordinary and extraordinary optical axis refractive indices of no = 2.2108, ne = 2.1373 at 1560 nm, and no = 2.2580, ne = 2.1778 at 780 nm [28]. The substrate material of the wafer is silicon dioxide (SiO₂), with a material refractive index of 1.4439 at 1560 nm and 1.4537 at 780 nm [29]. When the light field is transmitted in the curved waveguide, and the refractive index along the xyz direction on the cross section are ${n_x} = {(\frac{{{{\sin }^2}\alpha }}{{n_0^2}} + \frac{{{{\cos }^2}\alpha }}{{n_e^2}})^{\textrm{ - }\frac{1}{2}}}$, ${n_y} = {n_0}$ and ${n_z} = {(\frac{{{{\cos }^2}\alpha }}{{n_0^2}} + \frac{{{{\sin }^2}\alpha }}{{n_e^2}})^{\textrm{ - }\frac{1}{2}}}$, where α is the angle between the optical axis and the transmission section of the optical field. The illustration in Fig. 1(b) shows the numerical simulation results of the effective refractive index of the curved waveguide. The horizontal axis is the angle between the wave vector and the ordinary optical axis, and the vertical axis is the effective refractive index of bend waveguide. Because of the variable refractive index of the bend waveguide, mode hybridization occurs when the effective refractive index of the two eigenmodes of the waveguide is very close, which is similar to mode hybridization caused by the change of waveguide width [30].

Figure 1(c) and (d) show the numerical simulation results of the effective refractive index of the pump and SH target transport modes and orthogonal modes to them. We see that the effective refractive index of TE₀ mode and TM₀ mode of the pump is far different, so there is no mode hybridization and crosstalk in the transmission process. However, the effective refractive index curves of the SH light of TE₂ and TM₂ mode show a cross phenomenon in the blue circle, that is, mode hybridization will occur. It is worth noting that this simulation result has no relation to the bending radius, that is, we can’t eliminate the phenomenon of mode hybridization by changing the bending radius. However, the phase difference between the two modes transmitted can be controlled by changing the radius, and this mode hybridization will cancel out when the phase difference is just enough to produce constructive interference between the two modes. Figure 1(e) shows the finite-difference time-domain (FDTD) simulation results for input TE₂ mode in a 180 degree bend waveguide with different bending radius. The illustration shows the electric field distribution perpendicular to the transmission plane at radii of 26 µm and 30 µm. We see that the TE₂ mode and TM₂ mode produce the most constructive interference when the bending radius is 26 µm, with almost no intermode crosstalk after transmission in a 180 degree bend. This result makes the design of TE₂ mode directional couplers easier, and can improve the quality factor and extinction ratio of TE₂ mode transmission in the microring.

Efficient simultaneous coupling of two distinct optical frequencies poses a significant challenge in nonlinear microring resonators. Realizing maximum normalized conversion efficiency in SHG microrings necessitates meeting critical coupling conditions for both the pump and SH waves. In our proposed device (Fig. 1(a)), the pump and SH input and output are facilitated through a directional coupler (DC) at the top and an asymmetric directional coupler (ADC) at the bottom, respectively. As illustrated in Fig. 2(a), the 1560 nm pump couples to the RMR via a 180-degree bent waveguide. Capitalizing on the evanescent field disparity between the 1560 nm TE₀ and 780 nm TE₂ modes, FDTD simulations (Fig. 2(b)) demonstrate a coupling coefficient of 0.05 for the 1560 nm TE₀ mode when the coupling gap g = 0.7 µm, satisfying critical coupling. The coupling coefficient for the 780 nm TE₂ SH mode is an order of magnitude smaller, minimally compromising the quality factor.

 

Fig. 2. (a) Schematic diagram of the DC at the top of the RMR. (b)FDTD simulation results of the DC for 1560 nm pump and 780 nm SH. (c) Schematic diagram of the ADC at the bottom of the racetrack microring. The variation curves of ADC wide waveguide width w_s2 (d) and coupling gap g_z (e) with propagation length z. (f) FDTD simulation results of the ADC for 1560 nm pump and 780 nm SH.

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The second harmonic (SH) generated by nonlinear interaction in the RMR is a high-order TE₂ mode. This can be coupled to the bus waveguide and converted into the fundamental TE₀ mode using an asymmetric directional coupler (ADC). This reduces transmission loss of the SH mode and avoids unpredictable losses caused by directly coupling the high-order mode with the fiber at the chip's end face. In conventional ADCs, light can be coupled from one waveguide to another when the propagation constants of the eigenmodes in the two waveguides match. Considering the technological immaturity of lithium niobate etching, deviation in the waveguide width often arises from process instability. However, shortcuts to adiabaticity (STA) offer directional couplers with short device lengths and large fabrication tolerances [31,32]. The shape of the STA-enabled ADC at the RMR bottom is optimized using fast adiabatic evolution theory for efficient SH output generated via nonlinear conversion in the ring. The structure of the STA-ADC is depicted in Fig. 2(c), coupling the single-mode TE₀ narrow waveguide and multi-mode TE₂ wide waveguide. The electric field amplitudes E_s1 and E_s2 in the narrow and wide waveguides, respectively, evolve along the propagation length z according to the coupling mode equations:

3. Device fabrication and experimental test results

Figure  3(a) presents the metallographic microscope image and scanning electron microscope (SEM) image of the coupling region in the fabricated RMR. The double-resonance RMR was prepared on a 300 nm thick X-cut LNOI substrate (by NanoLN). A 100 nm Cr metal layer was first deposited on the lithium niobate surface by electron beam evaporation (EBE) to serve as a hard mask for lithium niobate etching. Electron beam lithography (EBL) then defined the pattern on electron beam resist spun over the Cr layer. This pattern was sequentially transferred to the Cr and lithium niobate layers via inductively coupled plasma reactive ion etching (ICP-RIE) using Cl₂ and Ar gases, respectively, fully etching through the 300 nm lithium niobate layer. Finally, 3 µm of SiO₂ was deposited by plasma enhanced chemical vapor deposition (PECVD) at 300°C as a cladding layer.

 

Fig. 3. (a) Metallographic microscope image of the racetrack microring resonator. Scanning electron microscope (SEM) images showing (b) the coupling region at the top and (c) the coupling region at the bottom.

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The experimental setup for linear and nonlinear characterization of the RMR is illustrated in Fig. 4(a). A C-band telecommunication source and a near infrared broadband source were utilized for linear characterization. A 1560 nm narrow linewidth laser (NKT Koheras Boostik E15) with 1 nm tuning range serves as the pump to generate second-harmonic (SH) light. The pump is amplified by an erbium-doped fiber amplifier (EDFA) and its polarization is controlled by a polarization controller (PC) to ensure TE polarization on-chip. The sample is mounted on a thermoelectric cooler (TEC) to achieve double resonance via heating. The pump and SH light are coupled on and off chip through lensed fibers (LF). On the chip, we created a wider waveguide with the same end coupler as the RMR, for which the transmission loss of the waveguide can be ignored. The coupling efficiency between the chip and the fiber was obtained by measuring the input and output optical power. The coupling losses measured in the experiment were 5.18 dB/facet at 1560 nm and 9 dB/facet at 780 nm. At the same time, we measured waveguides of different lengths and obtained losses of 1.5 dB/cm at 1560 nm and 2 dB/cm at 780 nm by measuring the transmission. After separation from residual pump light via a wavelength division multiplexer (WDM), the collected SH is spectrally analyzed by an optical spectrum analyzer (OSA). A 1560 nm photodetector (PD) monitors the pump power.

 

Fig. 4. (a) Experimental setup diagram. (b) Resonance spectra of the microring resonator at 28°C, with the black line representing the pump band and the red line representing the second-harmonic band. Transmission spectra under double resonance condition for (c) the 1560 nm pump light and (d) the 780 nm second-harmonic light.

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The RMR was first linearly characterized using a broadband light source covering the telecommunication and near infrared bands. The resonant wavelengths of the RMR can be expressed as ${\lambda _t} = {\lambda _{t0}} + {d_t} \cdot T$ and ${\lambda _v} = {\lambda _{v0}} + {d_v} \cdot T$ for the telecommunication and near infrared bands, respectively, where ${d_t} = 0.028nm/K$ and ${d_v} = 0.022nm/K$ denote the thermal-optic coefficients of the resonant spectra. Due to the disparity between ${d_t}$ and ${d_v}$, increasing the RMR temperature gradually reduces the wavelength detuning $\Delta \lambda = {\lambda _t} - 2{\lambda _v}$. At $\Delta \lambda = 0$, the two cavity resonant wavelengths satisfy the energy conservation requirement for ${\lambda _t} = 2{\lambda _v}$, achieving double resonance. As depicted in Fig. 4(b), setting the RMR temperature to 28°C aligns the resonant peaks at 1560.4 nm and 780.2 nm, fulfilling the double resonance condition. Figure 4(c) and 4(d) exhibit the resonant spectra under double resonance with loaded quality factors of ${Q_t} = 1 \times {10^5}$ and ${Q_v} = 2.8 \times {10^4}$ for the pump and second-harmonic, respectively.

The RMR was then nonlinearly characterized using a continuous 1560 nm narrow linewidth laser. Due to instabilities in the fabrication, some deviations exist between the fabricated and designed device dimensions. In principle, the SHG efficiency in the waveguide can be expressed as:

 

Fig. 5. (a) SH power versus waveguide width for straight waveguides. (b) Comparison of SHG in single-resonant microring resonator at 28°C and double-resonant microring resonator at 45°C. (c) SHG contrast between direct waveguide and microring resonator at identical pump power. (d) On-chip SH power as a function of the squared pump power.

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SHG was then experimentally characterized in the optimally-width RMR to ensure maximum phase matching. At 28°C, the resonance spectrum fulfilled the double resonance condition for energy conservation, as shown in Fig. 5(b). The measured SH power was -36.4 dBm. Heating to 45°C detuned the double resonance by adjusting the pump wavelength to resonance, yielding -46.6 dBm SH power. Hence, double resonance provides a 10.2 dB enhancement in SHG efficiency compared to the single resonance state. The illustration in Fig. 5(b) depicts SHG in our RMR pumped at 1560 nm, with 780 nm near infrared light generated through second-order nonlinearity and captured by a CCD above the chip. A conspicuous red spot is observable at the chip's output facet coupled to the lensed fiber, shown at right. A 4 mm long straight waveguide with the same phase matching design was fabricated near the RMR to serve as a control. Figure 5(c) contrasts SHG in the straight waveguide and double-resonant RMR at the same pump power. The RMR affords a 25.73 dB increase in efficiency over the waveguide. Figure 5(d) shows the quadratic SH power dependence on pump power; the blue dots are experimental data and the red line denotes a quadratic fit. Under low pump power, the on chip SHG power ${P_{SH}}$ follows ${P_{SH}} \propto P_{pump}^2$, with a linear fit slope of 1.01 confirming the expected quadratic scaling. The normalized SHG efficiency is $\eta = \frac{{{P_{SH}}}}{{P_{pump}^2}} = 9972\%/W$. When the square of the pump optical power exceeds 0.3mW², the SH power no longer increases. This saturation may be caused by the frequency-doubled light conversion efficiency reaching its limit. Another important reason is that the SH light power generated in the cavity becomes high enough to lead to the inverse process of SHG (that is, optical parametric oscillation) whereby the SH light gets converted back to the pump wavelength [33]. Additionally, high intra-cavity power can produce photorefractive effects that detune the resonator, destroying the phase matching and energy conservation conditions. The high achieved conversion efficiency stems from optimized pump and SH coupling, and double resonance. Further improving lithium niobate etching to reduce waveguide loss can improve the quality factor and enhance efficiency.

4. Conclusion

In conclusion, we have designed a racetrack microring resonator on X-cut lithium niobate on insulator for enhanced second-harmonic generation through modal phase matching. Independent coupling of the pump and second-harmonic enables near critical coupling for both. Optimizing the bending radius in the microring resonator averts detrimental mode hybridization effects on stable high-order mode second-harmonic transmission, further improving its quality factor. Fabrication on the lithium niobate on insulator chip was performed via electron beam lithography and dry etching. At 28°C, double resonance was attained in the microring, yielding a normalized second-harmonic generation efficiency of 9972%/W. Compared to a 4 mm straight waveguide with identical mode phase matching design in our experiment, the resonator demonstrates a 25.73 dB enhancement in SHG. Moreover, the X-cut configuration readily allows on-chip transverse electrodes for electro-optic control. Our work paves the path toward integrated generation of two-photon entanglement and complex quantum photonic circuits.